In various members subjected to the repeated heat cycle between high temperature and low temperature, heat expansion and contraction are repeated, as a result both of the members themselves and peripheral members of them are added with strain or stress, and consequently fracture by thermal fatigue is prone to occur. In such a circumstance, the fracture by thermal fatigue is hardly to occur in an alloy having a lower thermal expansion coefficient, because heat strain and heat stress to be added become smaller. As a known method for decreasing the thermal expansion coefficient, use of Magneto-volume effects is given. This is a method for decreasing the thermal expansion coefficient in such a way that when temperature is decreased, strain corresponding to a level of essentially contracted strain is compensated by magnetostriction due to generation of Atomic magnetic momentum or change in amount of the momentum. To obtain such magneto-volume effects, temperature dependence of the generation or the change in amount of the atomic magnetic-momentum is important. For example, in Fe-36% Ni Invar alloy used for a shadow mask in a cathode ray tube of a display, since the amount of the Atomic magnetic momentum suddenly changes near the Curie temperature (230 to 279° C.), a sudden decrease in thermal expansion coefficient is exhibited at a temperature lower than the Curie temperature (a value of thermal expansion coefficient of the alloy at about 200° C., at which the alloy is used for the shadow mask, is extremely low, about 1×10−6/° C.) However, the alloy has an extremely high thermal expansion coefficient of about 18×10−6/° C. at 800° C., which is in at the same level as in a typical austenitic stainless steel. Furthermore, the alloy contains Ni as much as 36%, resulting in an extreme increase in cost, consequently it is hard to be used for such an application in general consumer goods. From such reasons, Fe—Cr base alloys are widely used for the application. However, the Fe—Cr base alloys have a small temperature dependence of amount of the Atomic magnetic momentum is small, therefore the Magneto-volume effect is not observed even at a temperature of the Curie temperature or lower. In this way, decrease in thermal expansion coefficient due to Magneto-volume effect is difficult in the Fe—Cr base alloys. Therefore, in the related art, thermal fatigue life has been improved by a method using improvement in strength or high ductility by forming a high alloy (JP-A-2003-213377 and JP-A-2002-212685). However, improved strength by forming the high alloy necessarily causes a problem of reduction in workability, and orientation of high ductility causes strength to be extremely lowered, consequently it is pointed that another problem (for example, fatigue at elevated temperature) may occur. From such a situation, a new method has been strongly required for improving the thermal fatigue life by reducing the thermal expansion coefficient of Fe—Cr ferritic alloys.